Labor Market Structure and College Choices

Transcription

1 Labor Market Structure and College Choices Hakki Lee October 21, 2014 Abstract Using empirical evidence from South Korea and the U.S., this paper examines the idea that individuals might make schooling choices taking into account job mobility in the labor market. Low job mobility leads individuals to get more education so that they can get the first best job. In order to measure the role of labor market transition rates, I analyze a standard labor search model with college choice and with wages determined via Nash bargaining. I show that the labor market transition rates such as employment-to-employment (EE) and unemployment-to-employment (UE) affect an individual s schooling choice prior to labor market entry through two channels: the career-value channel and the wage channel. The model is calibrated to match the differences in college attainment between the U.S. and South Korea. The main result is that lower transition rates induce a higher share of college graduates. Moreover, compared to changes in UE transition rates, changes in EE transition rates have a bigger effect on changes in the share of college graduates. Keywords: Schooling choice, Education, Labor market search, Job mobility JEL Classification: E24, I21, J24, J31, J62, I am grateful to Daniele Coen-Pirani, Marla Ripoll, Todd Schoellman, Lutz Hendricks, Sewon Hur, and James Cassing for their comments. I have also benefited from comments by seminar participants at the University of Pittsburgh. All errors and shortcomings are mine alone. University of Pittsburgh; hal42@pitt.edu 1

2 1 Introduction The recent OECD report on education shows that, among 25- to 64-year olds, the average tertiary education attainment in OECD countries, is 33 percent. Among the 35 countries on the list, South Korea has an outstanding attainment rate of 41 percent, which is equal to the rate in the U.S. Furthermore, the difference between South Korea s rate and the OECD average is even larger for the younger generations. Between ages 25 and 34, the OECD average is 39 percent, while in South Korea it is 64 percent, the highest rate among the OECD countries. The literature that focuses on explaining the cross-country differences in education attainment mainly emphasizes the role of skill prices, education quality, public education subsidies, tuition and demographics. However, one aspect of the South Korean labor market that might have implications for college attainment is that it has high labor market rigidity. Due to its labor market structure, South Korean society has different norms for education: South Koreans perceive getting a job with satisfactory prospects as a one-shot game. According to an article in The Economist,...those who score well [on the college entrance exam] can enter one of South Korea s best universities, which has traditionally guaranteed them a job-for-life as a high-flying bureaucrat or desk warrior at a chaebol (conglomerate). Those who score poorly are doomed to attend a lesser university, or no university at all. They will then have to join a less prestigious firm and, since switching employers is frowned upon, may be stuck there for the rest of their lives. This quote highlights the role of labor market rigidities as an alternative channel for inducing higher schooling, which has not received much attention in the literature. This raises the question: What role does labor market structure play in individuals schooling choices? Many papers in the literature focus on skill prices as an important factor in explaining the evolution of educational attainment. However, a number of authors, such as Carneiro and Heckman (2003) and Goldin and Katz (2008), have pointed out that the sensitivity of college attainment to the increase in the college premium has been weak since the 1980s. They state that factors other than skill prices, such as education costs or quality of education, should be taken into consideration. However, when the economies of the U.S. and South Korea are compared, they show similarities in education costs and the college premium, despite the fact that college attainment in the U.S. is lower than in South Korea. This suggests that the differences in their labor market structures might play a partial role in the differences in their college attainment rates. I also find some empirical evidence to 2

3 support this idea. In particular, the differences in the labor market transition rates are quite large between these countries. While the average annual employment-to-employment (EE) transition rate in the U.S. is 13 percent, the same rate in South Korea is only four percent. Similarly, the unemployment-to-employment (UE) transition rate in the U.S. is 15 percent higher than in South Korea. 1 In order to capture an economy in which individuals take labor market structures into account when they make schooling choices, I introduce a model based on Flinn and Mullins (2013). While standard models in the education investment literature use competitive market models, Flinn and Mullins (2013) analyze schooling choices using a standard labor model with on-the-job search, in which wages are determined via Nash bargaining. The advantage of this model is that it allows me to have endogenous EE and UE transition rates and to analyze their effect on college choices. The effect of a change in the labor market transition rates on the share of college graduates is through the following two channels. First, an increase in the transition rates decreases the value of unemployment for the individual because the worker receives more job offers, and she can easily transition to better jobs while she is employed. In this model, college education is costly, so an individual will decide to go to college only if the difference between the expected value of the labor market careers for college and high school graduates exceeds this cost. Therefore, only those agents with abilities greater than the cutoff ability level will acquire a college degree. The decrease in the value of unemployment decreases the difference between the expected value of the labor market careers for college and high school graduates, and this increases the cutoff ability level. As a result, there is a decrease in the share of college graduates. I call this the career-value channel. The second channel works through wages. In standard competitive models, wages are determined according to the marginal product of labor that does not change with respect to the changes in the labor market structure. However, when wages are determined via Nash bargaining, then the slope of the wage function does change as the labor market transition rates change. Specifically, when there are high transition rates, the wage function becomes steeper over the range of match productivity. As individuals get more offers and face 1 While the U.S. labor market system is often characterized by highly mobile labor and relatively unregulated firms (Freeman, 2007), labor market flexibility in South Korea is relatively low and highly regulated. Edmans et al. (2014, Table 1b) reports the labor market flexibilty among OECD countries as measured by the OECD s Employment Protection Legislation (EPL) and data from the Fraser Institute s Economic Freedom of the World (EFW). In this table, the overall EPL score of South Korea is and the EFW score is 4.376, whereas for the U.S. they are and 8.673, respectively (high EPL implies low labor market flexibility and high EFW indicates a more flexible labor market). Moreover, they show that labor turnover rates are negatively correlated (-0.73) with the EPS index, which is consistent with other papers, such as David et al. (2007) and Messina and Vallanti (2007). 3

4 relatively steeper wage schedules, they climb up the wage ladder faster. High mobility helps individuals obtain higher wages, even with a lower education level. This makes individuals choose less schooling. I quantitatively solve the model and carefully calibrate it for the U.S. economy to match the share of college graduates, as well as other important labor market characteristics, such as EE and UE transition rates, the college premium, unemployment benefits, and the variance of log weekly wages. The calibrated model implies that the share of college graduates in the U.S. is around 35 percent, which exactly matches the value in the data. The main finding of this paper is that the differences in labor market transition rates can explain a significant portion (81 percent) of the difference in the college shares between the U.S. and South Korea. When the transition rates are reduced to the levels in South Korea, I find a lower share of college graduates - 44 percent. In the data, the share of four-year college graduates in South Korea is 46 percent. The second finding of the paper is that the EE transition rate has a larger impact on college choice. To show this, I decompose the effects of each transition rate on the share of college graduates. I find that when the model is calibrated to the EE transition rate in South Korea, keeping everything else the same as in the U.S. economy, the changes in the EE transition rate can explain almost the entire difference (73 percent) in the level schooling. On the other hand, the change in the UE transition rate has a small effect, accounting for only nine percent of the gap. To my knowledge, this is the first paper in the literature that quantitatively explores the connection between labor market structure and schooling choice using a model that has wages determined through a Nash bargaining problem. A number of papers have explored the effect of labor market flow rates on labor market outcomes, such as wages, or have focused on the pattern of the market flow rates themselves, such as Mincer and Jovanovic (1982), Blanchard et al. (1990), Topel and Ward (1992), Royalty (1998), Farber (1999), Stewart (2002), Nagypál (2008), and Shimer (2005, 2012). However, little has been done on the case of schooling investment. This paper contributes to this literature by also looking at the effects on schooling choice. In addition, this paper relates to a growing literature on the determinants of schooling. In particular, it relates to other papers on the evolution of schooling over time (Heckman et al., 1998; Lee and Wolpin, 2010; Restuccia and Vandenbroucke, 2013; Castro and Coen-Pirani, 2014) and on schooling across countries (Hendricks, 2010; Schoellman, 2012; Córdoba and Ripoll, 2013). These papers either emphasize the role of skill prices to explain the evolution of schooling across time or consider other determinants such as education quality, schooling costs, borrowing constraints, etc. As mentioned above, this paper complements this literature by taking into account another 4

5 factor: labor market structure. The current paper is the most closely related to the papers on the relationship between schooling choice and labor market characteristics, such as Zaharieva (2013) and Flinn and Mullins (2013). Zaharieva (2013) theoretically studies the relationship between the duration of schooling and labor market search frictions. She shows that people attain more education in the case of a labor market without on-the-job search than with on-the-job search. Intuitively, this implies that the labor market transition rates may affect educational enrollment. However, she assumes exogenous labor market transition rates. My model explains schooling choice in an economy with endogenous transition rates. Flinn and Mullins (2013) extends the standard search and matching model to allow for endogenous schooling choice. Even though they focus mainly on the linkage between the minimum wage and schooling decisions, they also show that labor market characteristics such as market contact rates, unemployment benefit, and match quality affect an individual s schooling decision. However, I emphasize the role of transition rates themselves on schooling choices. The remainder of the paper is organized as follows: Section 2 presents the data and the main factors; Section 3 introduces the model; Section 4 describes the empirical implementation; Section 5 shows the results of the benchmark model and counterfactual analysis; and, finally, Section 6 summarizes the conclusions. 2 Empirical Evidence Section 2.1 presents the stylized facts about college attainment in the U.S. and South Korea. Sections provide an overview of the driving forces that explain the difference in the share of college graduates across countries. The data sources for educational attainment and labor market transition rates are the March Current Population Surveys (CPS) for the U.S. and the Korean Labor and Income Panel Study (KLIPS) for South Korea Share of College Graduates The main objective of this paper is to explain the difference in educational attainment across countries. Of particular interest is the share of college graduates in the U.S. and South Korea. 3 The pattern of educational attainment is well-known and has been documented elsewhere (see, for example, Goldin and Katz (2008, Figures 7.1, 7.2 and 9.2); Hendricks 2 See Appendix A.1 for a description of the samples. 3 College graduate is defined as having at least a four-year college degree. 5

6 and Schoellman (2014, Figure 1a); and Castro and Coen-Pirani (2014, Figure 1a)). The case of South Korea is particularly interesting, because the economy went through a rapid development in the last 50 years and, together with economic development, the share of college graduates rose dramatically. My primary focus is on the share of college graduates for 2008 in both countries. If I look at the share of college graduates among individuals aged 33, in South Korea, 45 percent have completed a four-year degree, compared to 35 percent in the U.S. U.S. South Korea A. EE Transition Rate - HS Graduates College Graduates B. UE Transition Rate - HS Graduates College Graduates Table 1: Annual Labor Market Transition Rates 2.2 Labor Market Transition Rates Table 1 displays the labor market transition rates at the age of 33 for the U.S and South Korea. I use transition data constructed from the March CPS, , for the U.S. and from the KLIPS, , for South Korea. 4 Panel A shows EE transition rates across college and high school graduates. I define the EE transitions as job changes in which employed workers leave for a job with a different employer. While the EE transition rates in the U.S. are around 12 percent for high school graduates and 15 percent for college graduates, 5 the corresponding rates in South Korea are around four percent for both education groups. The key finding from this panel is the significant difference between the U.S. and South Korea, regardless of the level of schooling. 4 Appendix A.2 contains the details of my procedure. 5 Those EE transition rates are declining (wihin a certain range between 20 and ten percent) over ages and these basic patterns are consistent with the analysis of many other authors, such as Royalty (1998), Stewart (2002), and Blanchard et al. (1990). 6

7 Panel B shows the UE transition rates for both countries. The UE transition rates are defined as the proportion of workers who were unemployed in the previous year and are currently employed. Here, there is not a clear level difference across countries for all education groups; for instance, the transition rate for college graduates in South Korea is higher than that for high school graduates in the U.S. However, on average, the transition rates in the U.S. are higher than South Korea s. Age-group U.S. South Korea 20s s s s Table 2: Variance of log weekly wages 2.3 Variance of Log Weekly Wages Table 2 shows the variance of log weekly wages across age groups in the U.S and South Korea. I wanted to compare the variation of wages when people first enter the labor market, but the data do not contain enough information about the initial job for each individual. Thus, I group people based on their age. While the variance of log weekly wages for those in their 40s and 50s are similar in both countries, the variances for those in their 20s and 30s in South Korea are significantly larger. 6 Assuming that most of individuals in the sample go into labor force in their 20s, this captures that the young workers who enter the labor market in South Korea face a huge variation in wages compared to those in the U.S. This implies that the first job is more important in South Korea than in the U.S. 3 Model What factors related to labor market transition rates play a role in agents schooling decisions? How do differences in these factors affect the cross-country differences in the 6 See Appendix A.3 for more-detailed information about the sample. 7

8 share of college graduates? To answer these questions, I setup a simple, discrete time model based on Flinn and Mullins (2013) of search on-the-job in which individuals differ in terms of their ability and match productivity with firms. Agents obtain either high school or college education based on their ability, and the level of schooling that they acquire contributes to their productivity at work later in life. I use a partial equilibrium framework in which the match productivity distribution is assumed to be exogenous, and wages are determined by the generalized Nash bargaining problem. 3.1 The Benchmark Model Consider an economy populated by individuals who search for a job in discrete time and differ in their ability a according to a cumulative distribution function F (a). Individuals make a schooling decision prior to labor market entry. Individuals schooling decisions are binary and denoted by the subscript s, such that college education with s = 1 or high school only with s = 0. Based on their schooling level, individuals accumulate human capital h s. All individuals can either be unemployed or employed. If a worker is unemployed, she gets flow utility bah s, which refers to the unemployment benefit. The unemployment benefit is assumed to be based on the worker s ability a and her human capital h s. An unemployed worker has a chance to get a job with an exogenous contact rate λ U,s. An employed worker earns an endogenous wage, which is determined by the Nash bargaining problem. When a worker is employed, she faces layoff risk with probability δ s. If a worker is not separated from a current job, she gets an offer from another job with an exogenous contact rate λ E,s. 7 I assume that match productivity between a worker and a firm is given by y = ah s θ, where θ is the match productivity value between the worker and the firm, which is assumed to be independent and identically distributed each period from a known distribution G(θ). Hence, I have the worker s Bellman equations: 7 Flinn and Mullins (2013) assume that a worker has a chance to get an outside offer regardless of being separated from a current job. That is, layoff and job search are independent events. Unlike their model, here, I assume that a worker gets an offer from another job only when she is not separated from a current job. Once a worker is separated from a job, she will become an unemployed and get a new offer with a different arrival rate. 8

9 [ (1 W s (θ, ah s ; ω s ) = ω s + β(1 δ s )U s (ah s ) + βδ s λe,s (1 G(θ)) ) W s (θ, ah s ; ω s ) ] + λ E,s (1 G(θ)) W s (θ g(θ ), ah s ; ω s ) 1 G(θ) dθ, (3.1) θ θ where β is a discount factor. With a contact λ E,s a worker gets a new offer θ, and if θ > θ, she will accept it. The probability of accepting a new offer is denoted by 1 G(θ). Hence, the rate of EE transition is endogenously defined by λ E,s (1 G(θ)). Note that equation (3.1) can be rewritten as W s (θ, ah s ; ω s ) = ω s + β(1 δ s )U s (ah s ) + βδ s λ E,s W θ θ s(θ, ah s ; ω s )dg(θ ). (3.2) 1 βδ s + βδ s λ E,s (1 G(θ)) Now, consider the following value function for an unemployed worker. U s (ah s ) = ah s b + β(1 λ U,s (1 G(θs)))U s (ah s ) + βλ U,s (1 G(θs)) W s (θ g(θ ), ah s ; ω s ) (1 G(θs)) dθ, (3.3) θ θ s where θs is a reservation match productivity value for each schooling group. An unemployed worker gets a job offer with a contact rate λ U,s and she accepts the job if the match productivity value from the offer is greater than or equal to her reservation match productivity value. In the labor market, there is a continuum of firms that hire workers. Once a firm and a worker are matched, the outcome is the match productivity output y, and the firm pays wages for a worker. When a worker does not accept the outside job offer, the firm preserves the value of the matched job. 8 Hence, for a firm, the value of a matched job is ( J s (θ, ah s ; ω s ) = ah s θ ω s + βδ s 1 λe,s (1 G(θ)) ) J s (θ, ah s ; ω s ), (3.4) Note that equation (3.4) can be rewritten as J s (θ, ah s ; ω s ) = ah s θ ω s 1 βδ s + βδ s λ E,s (1 G(θ)). (3.5) 8 When a worker is separated from the job or leaves for another job, the firm needs to post a vacany. However, the free-entry condition drives the value of the unfilled job to 0. In this partial equilibrium setup, I do not track this vacancy. 9

10 solution: I assume that the equilibrium wage is determined by the generalized Nash bargaining max ω s ( Ws (θ, ah s ; ω s ) U s (ah s ) ) α Js (θ, ah s ; ω s ) 1 α, where α (0, 1) is the worker s bargaining power. 9 From the solution of the maximization problem, I derive the following equilibrium wages: [ ω s (θ, ah s ) = αah s θ + (1 α) (1 β)u s (ah s ) ( βδ s λ E,s Ws (θ, ah s ; ω) U s (ah s ) ) ] dg(θ ). (3.6) θ θ By the structure of the model, I can take ability a and human capital h out of all the value functions, such as W s (θ, ah s ; ω s ) = ah s W s (θ; ω s ), J s (θ, ah s ; ω s ) = ah s J s (θ; ω s ), and U s (ah s ) = ah s U s. Hence, the equilibrium wage can be rewritten as where ω s (θ) = ω s (θ, ah s ) = ah s ω s (θ), (3.7) [ ( )] ( ) αθ + (1 α) (1 β)u s βδ s λ E,s θ θ W s (θ ) U s dg(θ ). Since the decision of whether to accept the job offer when a worker is unemployed is characterized by θ s called the reservation match productivity value the following condition such that the value for the employed worker at θ s is equal to the value for the unemployed worker must hold: W s (θ s, ah s ; ω s ) = U s (ah s ). (3.8) which closes the model. 3.2 Schooling Choice Before entry into the labor market, an individual makes a schooling decision by comparing the expected value of the labor market career for each schooling level. The expected value of the labor market career for an individual with ability a and schooling s is given by U(ah s ). I assume that the baseline schooling level is a high school degree (s = 0). Without loss of generality, I normalize h 0 = 1 and h 1 = h > 1. Since I decompose U(ah s ) into ah s and U(θ) as constructed above, it is straightforward to find the condition for the optimal 9 I assume that the worker s bargaining power is the same across schooling groups: α 0 = α 1 = α. 10

11 schooling decision. To get a college degree, an individual incurs a total schooling cost of c. Then, an individual will decide to go to college only if the difference between the expected value of the labor market career for high school and college graduates exceeds the cost c: ahu 1 au 0 > c. For any college education fee c > 0, there exists a critical ability a such that a = c hu 1 U 0, (3.9) which implies that people with ability above a (a a ) acquire a college degree, and those who have ability below a (a < a ) obtain only a high school degree. Given that a is independent and identically distributed with a distribution function F (a), the share of college graduates is defined as 1 F (a ). 3.3 Labor Market Transition and Unemployment Rates Now, I solve for the unemployment rate implied by the model and show the inverse relationship between the unemployment and the UE transition rates. Let L denote the total population. Then, the total number of unemployed is Lu and the total number of employed is L Lu. Given u, the next period of unemployment u is computed as Lu = Lu ( 1 λ U,s (1 G(θ s)) ) + (L Lu)(1 δ s ), which means that total unemployment next period (u ) is equal to the number of unemployed workers who currently do not accept a job, plus the total number of employed workers who get separated from their jobs. In a steady state, u = u. Thus, the unemployment rate u can be defined as u s = 1 δ s 1 δ s + λ U,s (1 G(θ s)). (3.10) Note that 1 G(θ s) is an acceptance rate for an unemployed worker, such that a worker accepts the job offer only when the match quality with a job is higher than her reservation match productivity value. Together with a contact rate λ U,s, this shows the UE transition rate. As we saw in equation (3.10), the aggregate unemployment rate is decreasing in the UE transition. This negative relationship is straightforward by the definition of the 11

12 transition rate. 4 Empirical Implementation In this section, I first describe the solution algorithm and the calibration procedure and then discuss the predictions of the model for the share of college graduates. 4.1 Algorithm The model is solved on a grid for θ with the value for a worker W s (θ; ω), the value for an unemployed searcher U s, and the equilibrium wage ω s (θ). To solve the model numerically, I discretize θ into 200 equally-spaced grid points. θ [0, 1] is assumed to be log-normally distributed with log mean µ G and log standard deviation σ G. 1. Given θ s on the grids, compute the following equations, which are from equation (3.2), (3.3), and (3.6), respectively, assuming that initial values for U s and W s are zero. W s (θ; ω s ) = ω s(θ) + β(1 δ s )U s + βδ s λ E,s W θ θ s(θ ; ω s )dg(θ ) 1 βδ s + βδ s λ E,s (1 G(θ)) ω s (θ) = αθ + (1 α) ( 1 β + βδ s λ E,s (1 G(θ)) ) U s (1 α)βδ s λ E,s W s (θ ; ω s )dg(θ ) θ θ U s = b + βλ U,s W θ θs s (θ ; ω s )dg(θ ). 1 β + βλ U,s (1 G(θs)) In order to make it simple, let us substitute ω s (θ) into W s (θ; ω s ): where W s (θ) = 1 ] [αθ + B s (θ)u s + αβδ s λ E,s W s (θ )dg(θ ), (4.1) A s (θ) θ θ A s (θ) = 1 1 βδ s + βδ s λ E,s (1 G(θ)) (4.2) B s (θ) = (1 α)(1 β) + β(1 δ s ) + (1 α)βδ s λ E,s (1 G(θ)). (4.3) 2. Check whether those computed values for W s (θ) are equal to the initial values. If not, update those initial values of W s (θ) by taking the weighted average of the computed 12

13 values and the initial values and then iterate the same procedure until W s (θ) converges with each other. 3. Once W s (θ) converges for a given θs, I repeat step 1 and step 2 for all possible values of θs, which are the grid points on θ grids. 4. I find the optimal θ s that satisfies W s (θ s) = U s 5. Using the optimal θ s and U s for s = 0 and s = 1, I obtain a. 4.2 Setting the Model s Parameters I set a number of parameters a priori based on available evidence and calibrate the remaining parameters in order to match some key features of the U.S. data Parameters Set A-Priori Table 3 shows the parameters set a priori I target the U.S. labor market as a benchmark economy, considering monthly transition rates in particular. The annual interest rate is chosen to be four percent, which means that the discount factor β is set to be considering the monthly interest rate. The bargaining power of a worker α is assumed to be 0.72, which is a standard value, and the one used by Shimer (2005). For convenience, the separation rate for each schooling group is arbitrarily chosen within a range consistent with the literature. Shimer (2012) measures that quarterly average of monthly separation rate fluctuates around between two and five percent for the United States, using the Current Population Survey (CPS) 1948 to Using the CPS for January 1994 to August 2007, Nagypál (2008) shows that the separation rates are 0.86 percent and 0.45 percent for high school graduates and college graduates, respectively. Parameter Concept Values Source / Criteria β Rate of time preference % annual interest rate δ 0 Prob. of staying at the same job 0.98 Separation prob. 2% for a worker with HS degree Shimer(2012) δ 1 Prob. of staying at the same job 0.98 Separation prob. 2% for a worker with college degree Shimer(2012) α Bargaining weight of worker 0.72 Shimer(2005) Table 3: A-Priori Parameters 13

14 The distribution of ability is denoted by F, which is assumed to be lognormal with mean µ F and standard deviation σ F : a LN(µ F, σ 2 F ). Without loss of generality, the expected value of ability E[a] is normalized to one, which means that µ F = σ2 F 2. I also assume that the match productivity value between a firm and a worker is log-normally distributed according to the distribution function G with mean µ G and standard deviation σ G : θ LN(µ G, σg) 2. The expected value of the match productivity value E[θ] is normalized to one. This implies that µ G = σ2 G Calibration of Remaining Parameters ) I calibrate the remaining nine parameters (b, h, c, σ F, σ G, λ U,0, λ U,1, λ E,0, λ E,1 by targeting the nine moments listed below, including the share of college graduates and the labor market transition rates. The key to my calibration strategy is matching the share of college graduates and the labor market transition rates, such as EE and UE transition rates. I assume that those transition rates remain constant at the age-33 level when individuals age beyond 33. The nine moments targeted by the calibration procedure are: 1. Share of college graduates is computed by 1 F (a ): The empirical counterpart of this moment is The UE transition rate for each schooling group is computed by λ U,s (1 G(θs)), where s = 0, 1: The empirical counterparts of these moments are for high school graduates and for college graduates, respectively. 3. The EE transition rate for each schooling group is computed by λ E,s (1 G(θ)), where s = 0, 1: The empirical counterparts of these moments are for high school graduates and for college graduates, respectively. 4. The college wage premium relative to high school: The empirical counterpart of this moment is I define college wage premiums as the coefficients in regressions of individual level log weekly earnings 14

15 5. The unemployment benefit is computed by E[a s]hb E[ω s] : The empirical counterpart of this moment is The variance of log weekly earnings for each schooling group: The empirical counterparts of these moments are for high school graduates and for college graduates, respectively. Parameter Concept Calibrated parameter Target Value of target b Unemployment benefit % of wages h Human capital of college graduates College premium c Schooling costs Share of College Graduates σ F Log stddev. of ability dist Var. of log wages for HS σ G Log stddev. of match productivity dist Var. of log wages for College λ E,0 Prob. of getting new offer EE transition rates for employed with HS degree of HS graduates λ E,1 Prob. of getting new offer EE transition rates for employed with college degree of college graduates λ U,0 Prob. of getting new offer UE transition rate for unemployed with HS degree of HS graduates λ U,1 Prob. of getting new offer UE transition rate for unemployed with college degree of college graduates Table 4: Calibrated Parameters The values of parameters that govern each moment and the corresponding moments are shown in Table 4. The share of college graduates is informative for the schooling cost parameter c, and the standard deviation of the ability distribution σ F determines the dispersion in innate abilities. The UE transition rates for each schooling group are governed by the parameter governing the probability of an unemployed worker getting an job offer λ U,s. The EE transition rates are determined by the contact rates for an employed worker λ E,s. The college wage premium relative to high school graduates is informative for the parameter h determining the human capital of college graduates. The replacement rate is on a full set of dummies for potential experience and dummies for education groups, as in Autor et al. (2008). For more-detailed information on the college wage premium, see Appendix A.3. 15

16 governed by the parameter of unemployment benefit b. Since the wage of each schooling group depends on individuals abilities and the match productivity values, the earnings inequality among each group is informative for the parameters σ F and σ G, which determine the dispersion in innate ability and match productivity Simulation I discuss the procedure of calibrating the labor market transition rates in detail. Computing the UE transition rate is straightforward. Each individual has her own reservation match productivity value level θs according to her schooling level. If she is unemployed and gets an offer with probability λ U,s, she will decide whether or not to take it by comparing the reservation match productivity value with the one from an offer. However, the EE transition rate is not computed so simply. When an individual is currently working, she gets an offer for a new job with probability λ E,s. The decision to accept that offer depends on whether the new match productivity value is higher than current one. Since a worker s current match productivity value differs by the distribution of the value i.e., it is not fixed it cannot be computed directly. In order to compute the EE transition rate, I simulate the model for a population of 10,000 individuals. I assume that they are 18 years old in the first period and 56 in the last period. This generates 456 periods. High school graduates start looking for jobs right away, and college graduates start looking for jobs at age 22. I assume they are not in the labor force while they are in college. At the beginning of the simulation, all agents receive a random draw for their ability a that comes from the lognormal distribution with parameters that are listed above. I assume that in the first period, all agents are unemployed. Based on the value of a, agents that have their a greater than a are labeled as college graduates and the rest as high school graduates. Agents also receive a random draw of θ in every period with some probability, which determines the employment and job status in the next period. If the person is unemployed, the probability of receiving an offer is λ U,s and if the person is employed, the probability of receiving an offer is λ E,s. For every individual, these probabilities are also determined by random draws from a uniform distribution with parameters (0,1). In order to track EE changes, I keep a record of current θ, as well as of the employment status. In the beginning of the simulation and whenever an individual becomes unemployed, the current θ is equal to zero. I also generate random job separation draws (1 δ ) for every period and individual. If the job separation shocks are greater than 1 δ s, and the agent is 16

17 employed, then she becomes unemployed. If the agent is unemployed, she can be employed at t + 1 if she receives an offer and if the offer has a θ that is greater than θs. However, even during this period, there is a possibility that the match will be destroyed and that she will remain unemployed at t + 1, if 1 δ is greater than 1 δ s. At a given time t, when a high school (college) graduate is employed, she becomes unemployed at t + 1 if her 1 δ > 1 δ s. Then, her current θ at t + 1 is updated as her initial θ that she obtained at the beginning of the simulation. If, instead, 1 δ < 1 δ, then she will change jobs if she gets an offer and θ is greater than her current θ. This means at t + 1, her work status will remain employed, and her current θ will be equal to θ. If θ is less than her current θ, then there are no changes in her work status and θ state at t + 1. By keeping track of employment status and current θ for every period, I obtain the statistics related to unemployment, EE transitions and UE transitions. I compute these statistics at a monthly frequency. Moments Data Model Share of College Graduates College Premium (relative to high school) UE Transition Rate - HS Graduates College Graduates EE Transition Rate - HS Graduates College Graduates Variance of log wages - HS Graduates College Graduates Replacement Rate Table 5: Targeted Moments 17

18 Table 5 summarizes the moments used to calibrate the parameters and their predicted values. In the model, the UE transition rates are percent and percent for high school and college graduates, respectively. Note that the unemployment rates for each education group are determined by equation (3.10). Corresponding unemployment rates are 6.4 percent for high school graduates and 5.7 percent for college graduates. In the data, unemployment rate is 5.6 percent for high school graduates and 2.3 percent for college graduates. Overall, the model matches the nine moments very well. 5 Counterfactual Analysis I now discuss the implications of the model for the relationship between educational attainment and labor market transition rates. In the subsequent section, I first identify how to measure the labor market transition rates, and then I evaluate the contribution of changes in each transition rate to the share of college graduates. To do this, I take the U.S. economy as the benchmark economy and recalibrate only four contact rates to target the South Korean labor market transition rates, keeping all other parameters given. 5.1 Measure of the Labor Market Transition Rates for South Korea As discussed earlier, the labor market transition rates depend on the distribution of the match productivity values, as well as the contact probabilities. Thus, it is difficult to change those rates directly. However, each transition rate is an increasing function of the contact probabilities. Notice that the EE transition rate and the UE transition rate are defined as λ E,s (1 G(θ)) and λ U,s (1 G(θs)), respectively. Figure 1 shows that the labor market transition rates monotonically increase with the contact rates. The monotonicity of the function of the labor market transition rates allows me to change the contact rates to measure different transition rates. Table 5 presents the characteristics of the U.S. benchmark economy. The model is calibrated at a monthly frequency for the U.S. economy, but only yearly data are available for South Korea. I use the simulation to compute the yearly transition rates for the U.S., so that the transition rates in the two economies are comparable. In order to compute the yearly EE transition rates, I first find the total number of EE transitions that occur between ages 33 and 34 and divide this number by average monthly employment. Next, for the yearly UE transition rates, I simply calculate the total number of transitions from 18

19 HS Graduates College Graduates 0.4 HS Graduates College Graduates Employment to Employment Transition Rate Unemployment to Employment Transition Rate Contact Rate for Eemployed Contact Rate for Unemployed (a) EE Transition Rates (b) UE Transition Rates Figure 1: Labor Market Transition Rates Over Contact Rates unemployment to employment that occur between ages 33 and 34, divided by the number of unemployed people during the same period. ) Now, I recalibrate four parameters (λ U,0, λ U,1, λ E,0, λ E,1 to match the labor market transition rates for South Korea, keeping all other parameter values the same. Next, I experiment how much schooling increases compared to the case of the U.S. benchmark economy if I reduce the transition rates to the same level in South Korea. 5.2 Share of College Graduates and Labor Market Transition Rates Before presenting the main results from the counterfactual analysis, I first explain the mechanism of how changes in the labor market transition rates induce different shares of educational attainment. The effect of changes in the labor market transition rates on the share of college graduates is through two channels. 1. Career-value channel - Increases in the transition rates decrease the value of unemployment: The simple manipulation of equation (3.9) shows that the cutoff level of ability for schooling depends on the difference between the values for unemployment of each education group: ln a = ln c ln (hu 1 U 0 ). 19

20 1.18 x x a star a star Probability of getting new offer Contact Rate for Unemployed Worker (a) a over λ E (b) a over λ U Figure 2: Labor Market Transition Rates Over Contact Rates As can be seen from this equation, a depends on the gap between the education groups values for an unemployed searcher. When the transition rates increase, θ s decreases. Moreover, since the value of a future job for college graduates decreases more than for high school graduates when θ s decreases, the gap, hu 1 U 0, decreases, resulting in a low share of college graduates. Intuitively, if a worker faces many offers in the labor market, she may adjust her reservation match productivity value to a low level, so that she accepts jobs more easily. Since she knows that there are many chances to move between jobs in the future and that high job mobility will help her get higher wages in the future, having a lower reservation match productivity initially will be optimal. Furthermore, changes in the reservation match productivity value will also affect the value of being unemployed. The fact that the worker will accept jobs more easily means that the value to the worker of being unemployed is relatively low, because it is easier to move from unemployment to employment. Therefore, the decrease in the value of unemployment decreases the difference between the expected value of the labor market career for college and high school graduates and this increases the cutoff ability level. Consequently, I find a decrease in the share of college graduates. Figure 2 shows how the cutoff ability level changes over contact rates. In both panels, the cutoff level of ability is increasing as the contact rates increase. However, the magnitude of the effects are different. This is due to the difference in the definition of each transition rate. Unlike the EE transition rate, the UE transition rate depends on 20

21 the reservation value of match productivity. When λ U increases, people become less picky in choosing a job, which induces a decrease in the reservation value of match productivity. This implies a rise in the rate of acceptance (1 G(θs). However, quantitatively, the effect of the changes in θs on a is not uniform i.e., the effect is larger when λ U is small. This quantitative result will be particularly important when I analyze the role of each transition rate on the share of college graduates. 2. Wage channel - High transition rates tilt the wage schedule up: Figure 3 displays the change in ω(θ) over the match quality when the transition rates are high and low, respectively. I observe that the wage schedule under high transition rates is steeper than under low transition rates. This feature of the wage function comes from the Nash bargaining problem. In standard competitive models, wages are determined according to the marginal product of labor that does not change with respect to the changes in the labor market structure. However, when wages are determined via Nash bargaining, then the slope of the wage function does change as the labor market transition rates change. Figure 4a shows how ω(θ) changes over the match productivity value under high transition rates. This implies that when people enter the labor market with a low level of education, they can still enjoy high future wages, because they can move up along the wage function faster by getting more offers. However, under low transition rates, since people get fewer offers and face a relatively flatter wage schedule, it becomes difficult to move from a low-wage job to a high-wage job. This gives people a greater incentive to choose a college education. When job mobility is low, only higher education can help individuals increase their earnings. 5.3 Result Table 6 shows the results of the experiment, illustrating the effect of contact rates on schooling. I compare the results of the U.S. benchmark economy to those of the economy with South Korean transition rates, keeping all else constant. The first column shows the calibrated moments for the U.S. benchmark economy, and the second column reports the corresponding moments for the benchmark economy with South Korean transition rates. All the contact probabilities decrease to match the South Korean annual EE transition rates ( for high school graduates and for college graduates) and UE transition rates ( for high school graduates and for college graduates). Corresponding monthly transition rates are shown in the second column. I find that in the economy with South 21

22 9 8 High School College 9 8 High School College Wagebar 5 4 Wagebar Match productivity Match productivity (a) Under high transition rates (b) Under low transition rates Figure 3: Effect of Change in Transition Rates on Wage Korean transition rates, the EE transition rates fall by percent and percent for high school and college graduates, respectively. Similarly, the UE transition rates fall by percent for high school graduates and percent for college graduates. The changes in transition rates generate a percent increase in the share of college graduates. The corresponding unemployment benefit increases to I also find that the variance of log wages is also slightly higher for both education groups. Finally, the unemployment rate for high school graduates and college graduates increases significantly and becomes 13.7 percent and 7.45 percent for high school graduates and college graduates, respectively. Next, I decompose the effects of the changes in transition rates. The economy with South Korean EE transition rates shows larger effects than the economy with South Korean UE transition rates. While the economy with South Korean EE transition rates generates a percent increase in the share of college graduates, the economy with UE transition rates generates only a 2.97 percent increase in the share of college graduates. Changes in EE transition rates generate larger effects because if the concavity of the schooling function, as explained in Section 5.2. When the EE transition rate increases, the UE transition rate also increases, as shown in Panel B in Table 7; therefore, there is a lower unemployment rate and a higher unemployment benefit for both high school and college graduates. In panel C, lower UE transition rates also reduce the EE transition rates. As a result, unemployment increases and the unemployment benefit decreases for both schooling groups. The increase in the college premium is only 3.21 percent, which is less than half of the increase obtained in panel B. 22

23 EE Transition Rate U.S. Benchmark Economy B.E. with KOR Transition Rates λ E,0 = 0.260, λ E,1 = λ E,0 = 0.031, λ E,1 = λ U,0 = 0.685, λ U,1 = λ U,0 = 0.229, λ U,1 = Values Values % - HS Graduates College Graduates UE Transition Rate - HS Graduates College Graduates Share of College Graduates College Premium Unemployment benefit Variance of log wages - HS Graduates College Graduates Unemployment Rate - HS Graduates College Graduates note: % refers to the percentage change in the steady-state value of each moment under each alternative case compared to the value of the same moment under the benchmark economy. Table 6: Effects of Changes in Labor Market Transition Rates on Schooling 6 Conclusion This paper measures the role of labor market structures, such as EE and UE transition rates, in accounting for cross-country differences in the share of college graduates. I compare the U.S economy with the South Korean economy. Both countries are useful laboratories for measuring the effect of labor market structures on schooling differences for the following reasons. First, these two economies show similarities in education costs and the college premium, despite the fact that the college attainment level in the U.S. is lower than in South Korea. Second, the differences in the labor market transition rates between these countries are quite large. 23

24 Panel A Panel B Panel C U.S. Benchmark Economy B.E. with KOR EE Rates B.E. with KOR UE Rates λe,0 = 0.260, λe,1 = λe,0 = 0.031, λe,1 = λe,0 = 0.260, λe,1 = λu,0 = 0.685, λu,1 = λu,0 = 0.685, λu,1 = λu,0 = 0.229, λu,1 = Values Values % Values % EE Transition Rate - HS Graduates College Graduates UE Transition Rate - HS Graduates College Graduates Share of College Graduates College Premium Unemployment benefit Variance of log wages - HS Graduates College Graduates Unemployment Rate - HS Graduates College Graduates note: % refers to the percentage change in the steady-state value of each moment under each alternative case compared to the value of the same moment under the benchmark economy. Table 7: Decomposition of Effects of Changes in Labor Market Transition Rates on Schooling 24